Family of genus 7 curves with automorphism group $C_2^3$

• Label: 7.8-5.0.2-2-2-2-2-2-2
• Genus: \(7\)
• Quotient genus: \(0\)
• Group: \(C_2^3\)
• Signature: \([ 0; 2, 2, 2, 2, 2, 2, 2 ]\)

Family Information

Genus:	$7$
Dimension of the family:	$4$

Cover

Quotient genus:	$0$
Number of branch points:	$7$
Signature:	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$

Group

Name:	$C_2^3$
Identifier:	$[8,5]$

Conjugacy class(es) of Refined passports

Refined passport label	Conjugacy classes
7.8-5.0.2-2-2-2-2-2-2.1	2, 2, 2, 2, 3, 5, 7
7.8-5.0.2-2-2-2-2-2-2.2	2, 2, 2, 2, 3, 6, 8
7.8-5.0.2-2-2-2-2-2-2.3	2, 2, 2, 2, 4, 5, 8
7.8-5.0.2-2-2-2-2-2-2.4	2, 2, 2, 2, 4, 6, 7
7.8-5.0.2-2-2-2-2-2-2.5	2, 2, 2, 3, 3, 5, 6
7.8-5.0.2-2-2-2-2-2-2.6	2, 2, 2, 3, 3, 7, 8
7.8-5.0.2-2-2-2-2-2-2.7	2, 2, 2, 3, 4, 5, 5
7.8-5.0.2-2-2-2-2-2-2.8	2, 2, 2, 3, 4, 6, 6
7.8-5.0.2-2-2-2-2-2-2.9	2, 2, 2, 3, 4, 7, 7
7.8-5.0.2-2-2-2-2-2-2.10	2, 2, 2, 3, 4, 8, 8
7.8-5.0.2-2-2-2-2-2-2.11	2, 2, 2, 4, 4, 5, 6
7.8-5.0.2-2-2-2-2-2-2.12	2, 2, 2, 4, 4, 7, 8
7.8-5.0.2-2-2-2-2-2-2.13	2, 2, 2, 5, 5, 7, 8
7.8-5.0.2-2-2-2-2-2-2.14	2, 2, 2, 5, 6, 7, 7
7.8-5.0.2-2-2-2-2-2-2.15	2, 2, 2, 5, 6, 8, 8
7.8-5.0.2-2-2-2-2-2-2.16	2, 2, 2, 6, 6, 7, 8
7.8-5.0.2-2-2-2-2-2-2.17	2, 2, 3, 3, 3, 5, 7
7.8-5.0.2-2-2-2-2-2-2.18	2, 2, 3, 3, 3, 6, 8
7.8-5.0.2-2-2-2-2-2-2.19	2, 2, 3, 3, 4, 5, 8
7.8-5.0.2-2-2-2-2-2-2.20	2, 2, 3, 3, 4, 6, 7
7.8-5.0.2-2-2-2-2-2-2.21	2, 2, 3, 4, 4, 5, 7
7.8-5.0.2-2-2-2-2-2-2.22	2, 2, 3, 4, 4, 6, 8
7.8-5.0.2-2-2-2-2-2-2.23	2, 2, 3, 5, 5, 5, 7
7.8-5.0.2-2-2-2-2-2-2.24	2, 2, 3, 5, 5, 6, 8
7.8-5.0.2-2-2-2-2-2-2.25	2, 2, 3, 5, 6, 6, 7
7.8-5.0.2-2-2-2-2-2-2.26	2, 2, 3, 5, 7, 7, 7
7.8-5.0.2-2-2-2-2-2-2.27	2, 2, 3, 5, 7, 8, 8
7.8-5.0.2-2-2-2-2-2-2.28	2, 2, 3, 6, 6, 6, 8
7.8-5.0.2-2-2-2-2-2-2.29	2, 2, 3, 6, 7, 7, 8
7.8-5.0.2-2-2-2-2-2-2.30	2, 2, 3, 6, 8, 8, 8
7.8-5.0.2-2-2-2-2-2-2.31	2, 2, 4, 4, 4, 5, 8
7.8-5.0.2-2-2-2-2-2-2.32	2, 2, 4, 4, 4, 6, 7
7.8-5.0.2-2-2-2-2-2-2.33	2, 2, 4, 5, 5, 5, 8
7.8-5.0.2-2-2-2-2-2-2.34	2, 2, 4, 5, 5, 6, 7
7.8-5.0.2-2-2-2-2-2-2.35	2, 2, 4, 5, 6, 6, 8
7.8-5.0.2-2-2-2-2-2-2.36	2, 2, 4, 5, 7, 7, 8
7.8-5.0.2-2-2-2-2-2-2.37	2, 2, 4, 5, 8, 8, 8
7.8-5.0.2-2-2-2-2-2-2.38	2, 2, 4, 6, 6, 6, 7
7.8-5.0.2-2-2-2-2-2-2.39	2, 2, 4, 6, 7, 7, 7
7.8-5.0.2-2-2-2-2-2-2.40	2, 2, 4, 6, 7, 8, 8
7.8-5.0.2-2-2-2-2-2-2.41	2, 3, 3, 3, 3, 5, 6
7.8-5.0.2-2-2-2-2-2-2.42	2, 3, 3, 3, 3, 7, 8
7.8-5.0.2-2-2-2-2-2-2.43	2, 3, 3, 3, 4, 5, 5
7.8-5.0.2-2-2-2-2-2-2.44	2, 3, 3, 3, 4, 6, 6
7.8-5.0.2-2-2-2-2-2-2.45	2, 3, 3, 3, 4, 7, 7
7.8-5.0.2-2-2-2-2-2-2.46	2, 3, 3, 3, 4, 8, 8
7.8-5.0.2-2-2-2-2-2-2.47	2, 3, 3, 4, 4, 5, 6
7.8-5.0.2-2-2-2-2-2-2.48	2, 3, 3, 4, 4, 7, 8
7.8-5.0.2-2-2-2-2-2-2.49	2, 3, 3, 5, 5, 5, 6
7.8-5.0.2-2-2-2-2-2-2.50	2, 3, 3, 5, 5, 7, 8
7.8-5.0.2-2-2-2-2-2-2.51	2, 3, 3, 5, 6, 6, 6
7.8-5.0.2-2-2-2-2-2-2.52	2, 3, 3, 5, 6, 7, 7
7.8-5.0.2-2-2-2-2-2-2.53	2, 3, 3, 5, 6, 8, 8
7.8-5.0.2-2-2-2-2-2-2.54	2, 3, 3, 6, 6, 7, 8
7.8-5.0.2-2-2-2-2-2-2.55	2, 3, 3, 7, 7, 7, 8
7.8-5.0.2-2-2-2-2-2-2.56	2, 3, 3, 7, 8, 8, 8
7.8-5.0.2-2-2-2-2-2-2.57	2, 3, 4, 4, 4, 5, 5
7.8-5.0.2-2-2-2-2-2-2.58	2, 3, 4, 4, 4, 6, 6
7.8-5.0.2-2-2-2-2-2-2.59	2, 3, 4, 4, 4, 7, 7
7.8-5.0.2-2-2-2-2-2-2.60	2, 3, 4, 4, 4, 8, 8
7.8-5.0.2-2-2-2-2-2-2.61	2, 3, 4, 5, 5, 5, 5
7.8-5.0.2-2-2-2-2-2-2.62	2, 3, 4, 5, 5, 6, 6
7.8-5.0.2-2-2-2-2-2-2.63	2, 3, 4, 5, 5, 7, 7
7.8-5.0.2-2-2-2-2-2-2.64	2, 3, 4, 5, 5, 8, 8
7.8-5.0.2-2-2-2-2-2-2.65	2, 3, 4, 5, 6, 7, 8
7.8-5.0.2-2-2-2-2-2-2.66	2, 3, 4, 6, 6, 6, 6
7.8-5.0.2-2-2-2-2-2-2.67	2, 3, 4, 6, 6, 7, 7
7.8-5.0.2-2-2-2-2-2-2.68	2, 3, 4, 6, 6, 8, 8
7.8-5.0.2-2-2-2-2-2-2.69	2, 3, 4, 7, 7, 7, 7
7.8-5.0.2-2-2-2-2-2-2.70	2, 3, 4, 7, 7, 8, 8
7.8-5.0.2-2-2-2-2-2-2.71	2, 3, 4, 8, 8, 8, 8
7.8-5.0.2-2-2-2-2-2-2.72	2, 4, 4, 4, 4, 5, 6
7.8-5.0.2-2-2-2-2-2-2.73	2, 4, 4, 4, 4, 7, 8
7.8-5.0.2-2-2-2-2-2-2.74	2, 4, 4, 5, 5, 5, 6
7.8-5.0.2-2-2-2-2-2-2.75	2, 4, 4, 5, 5, 7, 8
7.8-5.0.2-2-2-2-2-2-2.76	2, 4, 4, 5, 6, 6, 6
7.8-5.0.2-2-2-2-2-2-2.77	2, 4, 4, 5, 6, 7, 7
7.8-5.0.2-2-2-2-2-2-2.78	2, 4, 4, 5, 6, 8, 8
7.8-5.0.2-2-2-2-2-2-2.79	2, 4, 4, 6, 6, 7, 8
7.8-5.0.2-2-2-2-2-2-2.80	2, 4, 4, 7, 7, 7, 8
7.8-5.0.2-2-2-2-2-2-2.81	2, 4, 4, 7, 8, 8, 8
7.8-5.0.2-2-2-2-2-2-2.82	2, 5, 5, 5, 5, 7, 8
7.8-5.0.2-2-2-2-2-2-2.83	2, 5, 5, 5, 6, 7, 7
7.8-5.0.2-2-2-2-2-2-2.84	2, 5, 5, 5, 6, 8, 8
7.8-5.0.2-2-2-2-2-2-2.85	2, 5, 5, 6, 6, 7, 8
7.8-5.0.2-2-2-2-2-2-2.86	2, 5, 5, 7, 7, 7, 8
7.8-5.0.2-2-2-2-2-2-2.87	2, 5, 5, 7, 8, 8, 8
7.8-5.0.2-2-2-2-2-2-2.88	2, 5, 6, 6, 6, 7, 7
7.8-5.0.2-2-2-2-2-2-2.89	2, 5, 6, 6, 6, 8, 8
7.8-5.0.2-2-2-2-2-2-2.90	2, 5, 6, 7, 7, 7, 7
7.8-5.0.2-2-2-2-2-2-2.91	2, 5, 6, 7, 7, 8, 8
7.8-5.0.2-2-2-2-2-2-2.92	2, 5, 6, 8, 8, 8, 8
7.8-5.0.2-2-2-2-2-2-2.93	2, 6, 6, 6, 6, 7, 8
7.8-5.0.2-2-2-2-2-2-2.94	2, 6, 6, 7, 7, 7, 8
7.8-5.0.2-2-2-2-2-2-2.95	2, 6, 6, 7, 8, 8, 8
7.8-5.0.2-2-2-2-2-2-2.96	3, 3, 3, 3, 4, 5, 8
7.8-5.0.2-2-2-2-2-2-2.97	3, 3, 3, 3, 4, 6, 7
7.8-5.0.2-2-2-2-2-2-2.98	3, 3, 3, 4, 4, 5, 7
7.8-5.0.2-2-2-2-2-2-2.99	3, 3, 3, 4, 4, 6, 8
7.8-5.0.2-2-2-2-2-2-2.100	3, 3, 3, 5, 5, 6, 8
7.8-5.0.2-2-2-2-2-2-2.101	3, 3, 3, 5, 6, 6, 7
7.8-5.0.2-2-2-2-2-2-2.102	3, 3, 3, 5, 7, 8, 8
7.8-5.0.2-2-2-2-2-2-2.103	3, 3, 3, 6, 7, 7, 8
7.8-5.0.2-2-2-2-2-2-2.104	3, 3, 4, 4, 4, 5, 8
7.8-5.0.2-2-2-2-2-2-2.105	3, 3, 4, 4, 4, 6, 7
7.8-5.0.2-2-2-2-2-2-2.106	3, 3, 4, 5, 5, 5, 8
7.8-5.0.2-2-2-2-2-2-2.107	3, 3, 4, 5, 5, 6, 7
7.8-5.0.2-2-2-2-2-2-2.108	3, 3, 4, 5, 6, 6, 8
7.8-5.0.2-2-2-2-2-2-2.109	3, 3, 4, 5, 7, 7, 8
7.8-5.0.2-2-2-2-2-2-2.110	3, 3, 4, 5, 8, 8, 8
7.8-5.0.2-2-2-2-2-2-2.111	3, 3, 4, 6, 6, 6, 7
7.8-5.0.2-2-2-2-2-2-2.112	3, 3, 4, 6, 7, 7, 7
7.8-5.0.2-2-2-2-2-2-2.113	3, 3, 4, 6, 7, 8, 8
7.8-5.0.2-2-2-2-2-2-2.114	3, 4, 4, 4, 4, 5, 7
7.8-5.0.2-2-2-2-2-2-2.115	3, 4, 4, 4, 4, 6, 8
7.8-5.0.2-2-2-2-2-2-2.116	3, 4, 4, 5, 5, 5, 7
7.8-5.0.2-2-2-2-2-2-2.117	3, 4, 4, 5, 5, 6, 8
7.8-5.0.2-2-2-2-2-2-2.118	3, 4, 4, 5, 6, 6, 7
7.8-5.0.2-2-2-2-2-2-2.119	3, 4, 4, 5, 7, 7, 7
7.8-5.0.2-2-2-2-2-2-2.120	3, 4, 4, 5, 7, 8, 8
7.8-5.0.2-2-2-2-2-2-2.121	3, 4, 4, 6, 6, 6, 8
7.8-5.0.2-2-2-2-2-2-2.122	3, 4, 4, 6, 7, 7, 8
7.8-5.0.2-2-2-2-2-2-2.123	3, 4, 4, 6, 8, 8, 8
7.8-5.0.2-2-2-2-2-2-2.124	3, 5, 5, 5, 5, 6, 8
7.8-5.0.2-2-2-2-2-2-2.125	3, 5, 5, 5, 6, 6, 7
7.8-5.0.2-2-2-2-2-2-2.126	3, 5, 5, 5, 7, 8, 8
7.8-5.0.2-2-2-2-2-2-2.127	3, 5, 5, 6, 6, 6, 8
7.8-5.0.2-2-2-2-2-2-2.128	3, 5, 5, 6, 7, 7, 8
7.8-5.0.2-2-2-2-2-2-2.129	3, 5, 5, 6, 8, 8, 8
7.8-5.0.2-2-2-2-2-2-2.130	3, 5, 6, 6, 6, 6, 7
7.8-5.0.2-2-2-2-2-2-2.131	3, 5, 6, 6, 7, 7, 7
7.8-5.0.2-2-2-2-2-2-2.132	3, 5, 6, 6, 7, 8, 8
7.8-5.0.2-2-2-2-2-2-2.133	3, 5, 7, 7, 7, 8, 8
7.8-5.0.2-2-2-2-2-2-2.134	3, 5, 7, 8, 8, 8, 8
7.8-5.0.2-2-2-2-2-2-2.135	3, 6, 6, 6, 7, 7, 8
7.8-5.0.2-2-2-2-2-2-2.136	3, 6, 7, 7, 7, 7, 8
7.8-5.0.2-2-2-2-2-2-2.137	3, 6, 7, 7, 8, 8, 8
7.8-5.0.2-2-2-2-2-2-2.138	4, 4, 4, 5, 5, 6, 7
7.8-5.0.2-2-2-2-2-2-2.139	4, 4, 4, 5, 6, 6, 8
7.8-5.0.2-2-2-2-2-2-2.140	4, 4, 4, 5, 7, 7, 8
7.8-5.0.2-2-2-2-2-2-2.141	4, 4, 4, 6, 7, 8, 8
7.8-5.0.2-2-2-2-2-2-2.142	4, 5, 5, 5, 5, 6, 7
7.8-5.0.2-2-2-2-2-2-2.143	4, 5, 5, 5, 6, 6, 8
7.8-5.0.2-2-2-2-2-2-2.144	4, 5, 5, 5, 7, 7, 8
7.8-5.0.2-2-2-2-2-2-2.145	4, 5, 5, 6, 6, 6, 7
7.8-5.0.2-2-2-2-2-2-2.146	4, 5, 5, 6, 7, 7, 7
7.8-5.0.2-2-2-2-2-2-2.147	4, 5, 5, 6, 7, 8, 8
7.8-5.0.2-2-2-2-2-2-2.148	4, 5, 6, 6, 6, 6, 8
7.8-5.0.2-2-2-2-2-2-2.149	4, 5, 6, 6, 7, 7, 8
7.8-5.0.2-2-2-2-2-2-2.150	4, 5, 6, 6, 8, 8, 8
7.8-5.0.2-2-2-2-2-2-2.151	4, 5, 7, 7, 7, 7, 8
7.8-5.0.2-2-2-2-2-2-2.152	4, 5, 7, 7, 8, 8, 8
7.8-5.0.2-2-2-2-2-2-2.153	4, 6, 6, 6, 7, 8, 8
7.8-5.0.2-2-2-2-2-2-2.154	4, 6, 7, 7, 7, 8, 8
7.8-5.0.2-2-2-2-2-2-2.155	4, 6, 7, 8, 8, 8, 8

Displaying representatives for 4 topologically inequivalent actions.

7.8-5.0.2-2-2-2-2-2-2.1.1

	(1,2) (3,4) (5,6) (7,8)
	(1,2) (3,4) (5,6) (7,8)
	(1,2) (3,4) (5,6) (7,8)
	(1,2) (3,4) (5,6) (7,8)
	(1,3) (2,4) (5,7) (6,8)
	(1,5) (2,6) (3,7) (4,8)
	(1,7) (2,8) (3,5) (4,6)

7.8-5.0.2-2-2-2-2-2-2.5.1

	(1,2) (3,4) (5,6) (7,8)
	(1,2) (3,4) (5,6) (7,8)
	(1,2) (3,4) (5,6) (7,8)
	(1,3) (2,4) (5,7) (6,8)
	(1,3) (2,4) (5,7) (6,8)
	(1,5) (2,6) (3,7) (4,8)
	(1,6) (2,5) (3,8) (4,7)

7.8-5.0.2-2-2-2-2-2-2.19.1

	(1,2) (3,4) (5,6) (7,8)
	(1,2) (3,4) (5,6) (7,8)
	(1,3) (2,4) (5,7) (6,8)
	(1,3) (2,4) (5,7) (6,8)
	(1,4) (2,3) (5,8) (6,7)
	(1,5) (2,6) (3,7) (4,8)
	(1,8) (2,7) (3,6) (4,5)

7.8-5.0.2-2-2-2-2-2-2.65.1

	(1,2) (3,4) (5,6) (7,8)
	(1,3) (2,4) (5,7) (6,8)
	(1,4) (2,3) (5,8) (6,7)
	(1,5) (2,6) (3,7) (4,8)
	(1,6) (2,5) (3,8) (4,7)
	(1,7) (2,8) (3,5) (4,6)
	(1,8) (2,7) (3,6) (4,5)